Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = 3$ $a_i = -2a_{i-1}$ What is $a_{2}$, the second term in the sequence?
From the given formula, we can see that the first term of the sequence is $3$ and the common ratio is $-2$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = 3 \cdot -2 = -6$.